* Statistics: Any four from Stat 333, 424, 575, 641, and 642 [http://www.stat.wisc.edu/course-listing]

−

** Stat 333 has as a prerequisite some experience with statistical software. This can be achieved by also registering for Stat 327. Stat 327 is a single credit course which does not count for the mathematics major

+

** Stat 333 has as a prerequisite some experience with statistical software. This can be achieved by also registering for Stat 327. Stat 327 is a single credit course which does not count for the mathematics major.

** Note that 435, 475, 513, 514, 515, and 525 are crosslisted with math. They may not be used as both application courses and core mathematics courses

** Note that 435, 475, 513, 514, 515, and 525 are crosslisted with math. They may not be used as both application courses and core mathematics courses

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'''Application Courses'''

'''Application Courses'''

−

* Programming: CS 302 and 367.

+

* Programming: CS 300 and CS 400 (or CS 302 and 367).

−

** Students who are exempt from CS 302 should discuss an appropriate substitute with their adviser.

+

* One of the following two pairs:

* One of the following two pairs:

** The CS track: Operating systems (CS 537) and Security (CS 642)

** The CS track: Operating systems (CS 537) and Security (CS 642)

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The so called STEM fields continue to be a major area of interest and investment for education policy makers. In particular secondary education instructors with strong mathematics backgrounds are in demand across the nation in public, private, and charter school environments.

The so called STEM fields continue to be a major area of interest and investment for education policy makers. In particular secondary education instructors with strong mathematics backgrounds are in demand across the nation in public, private, and charter school environments.

−

The following program was designed for a math major who is interested in becoming an educator at the secondary level. Note that successful completion of the coursework outlined below would make a strong candidate for graduate work in mathematics and education at the masters level. Our own School of Education offers a [http://ci.education.wisc.edu/ci/academics/degree-options-certification-programs/wisconsin-masters-in-teaching/secondary-mathematics-masters Masters Degree in Secondary Mathematics] which concludes with state certification.

+

The following program was designed for a math major who is interested in becoming an educator at the secondary level. Note that successful completion of the coursework outlined below would make a strong candidate for graduate work in mathematics and education at the masters level. Our own School of Education offers a [http://www.uwteach.com/mathematics.html Masters Degree in Secondary Mathematics] which concludes with state certification.

−

Note that a major requires at least two courses at the 500 level and changing any of the courses listed below may prevent you from covering all of the content areas required for Wisconsin state certification. Therefore you should consider the suggestions below carefully.

+

''Note that a major requires at least two courses at the 500 level. Therefore you should consider the suggestions below carefully.''

'''Application Courses'''

'''Application Courses'''

−

* Statistics: [http://www.math.wisc.edu/node/114 Math 310]

* History and philosophy of mathematics: [http://www.math.wisc.edu/473-history-mathematics Math 473].

* History and philosophy of mathematics: [http://www.math.wisc.edu/473-history-mathematics Math 473].

−

* At least two additional courses from Computer Science, Physics, or Mathematics at the Intermediate or Advanced Level.

* Courses in computer programming, statistics, physics, economics, and finance can broaden your content areas and qualify you for more subjects.

* Courses in computer programming, statistics, physics, economics, and finance can broaden your content areas and qualify you for more subjects.

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A student who wishes to complete a major in statistics offered by the [https://www.stat.wisc.edu/undergrad/undergraduate-major-statistics Department of Statistics] should complete the program above and include:

A student who wishes to complete a major in statistics offered by the [https://www.stat.wisc.edu/undergrad/undergraduate-major-statistics Department of Statistics] should complete the program above and include:

* Stat 302 and 327.

* Stat 302 and 327.

−

* A course in programming (e.g. CS 302).

+

* A course in programming (e.g. CS 300).

* At least one more course from the statistics electives above.

* At least one more course from the statistics electives above.

Latest revision as of 17:32, 7 February 2018

The Option 2 math major requires six math courses and four courses in an area of application. These four courses are required to have a certain mathematical content. They should also form a coherent collection of courses that reflect a plan to study some discipline outside of mathematics that uses a fair amount of mathematics. The selection of the four courses, together with the six required math courses must be approved by the student's advisor. This page lists some sample packages in several popular areas.

Economics and Business

Actuarial Mathematics

Actuaries use techniques in mathematics and statistics to evaluate risk in a variety of areas including insurance, finance, healthcare, and even criminal justice. In recent history the field has been revolutionized by advances in the theory of probability and the ability to access, store, and process very large data sets.

Professional actuaries are currently in demand, have lucrative pay, and is a growth field [1]. Similar to some other fields (law, accounting, etc.) there are professional organizations which administer a series of examinations [2]. Oftentimes students complete some of these examinations before graduating which allows them to move right into a career (Note: these exams are not required for graduation).

Students who are interested in actuarial mathematics should consider coursework in probability, statistics, analysis, as well as computational mathematics.

Business

Applications of mathematics to business is often referred to as Operations Research or Management Science. Specifically, the goal is to use mathematics to make the best decisions in a variety of areas: searching, routing, scheduling, transport, etc.

The modern version of the field grew out of the work mathematicians did in order to aid the Allied war effort during world war II.[3] Since then, the field has grown into a robust and active area of research and scholarship including several journals and professional organizations.[4]

Students interested in applications of mathematics to business can find many employment opportunities in private corporations, government agencies, nonprofit enterprises, and more. Students can also move onto postgraduate programs in mathematics or business.

Economics

Economics is perhaps the most mathematical of the social sciences. Specifically economists wish to model and understand the behavior of individuals (people, countries, animals, etc.). Typically this is done by quantifying some elements of interest to the individuals.

Due to the quantitative nature of the field, economic theory has begun to move from the classic areas of markets, products, supply, demand, etc. and into many seemingly unrelated areas: law, psychology, political science, biology, and more.[5]

Regardless, the backbone of economics and economic theory is mathematics. The classical area of mathematics most often related with economics is analysis.

Finance

Financial mathematics is more popular than ever with financial firms hiring "quants" from all areas of mathematics and the natural sciences. Financial markets are of interest to mathematicians due to the difficult nature of modeling the complex systems. The standard tools involved are evolutionary differential equations, measure theory, and stochastic calculus.

Also:
Consider a program in Finance at the the Wisconsin School of Business.

Physical Sciences

The physical sciences and mathematics have grown hand-in-hand since antiquity.
Students with strong backgrounds in mathematics who are also interested in a branch of the physical sciences can find opportunities in laboratories, engineering firms, education, finance, law, business, and medicine. Those with very strong academic records can find themselves as preferred candidates for graduate study in their choice of field.

The following sample programs in mathematics have strong relationships with a particular area of interest in the natural sciences.

Atmospheric & Oceanic Sciences

Weather and climate is determined by the interaction between two thin layers which cover the planet: The oceans and the atmosphere. Understanding how these two fluids act and interact allow humans to describe historical climate trends, forecast near future weather with incredible accuracy, and hopefully describe long term climate change which will affect the future of human society.

A student interested in atmospheric and oceanic studies who has a strong mathematics background can find a career working in local, national, and international meteorological laboratories. These include private scientific consulting businesses as well as public enterprises. Students interested in graduate study could find their future studies supported by the National Science Foundation, the Department of Energy, NASA, or others [6]. There is a large amount of funding available in the area due to the relevance research findings have on energy and economic policy.

Mathematicians who work in Atmospheric and oceanic studies are drawn to the complexities of the problems and the variety of methods in both pure and applied mathematics which can be brought to bear on them. Students should take coursework in methods of applied mathematics, differential equations, computational mathematics, and differential geometry and topology.

Chemistry

The applications of mathematics to chemistry range from the mundane: Ratios for chemical reactants; to the esoteric: Computational methods in quantum chemistry. Research in this latter topic lead to a Nobel Prize in Chemistry to mathematician John Pople.

All areas of pure and applied mathematics have applications in modern chemistry. The most accessible track features coursework focusing on applied analysis and computational math. Students with a strong interest in theoretical mathematics should also consider modern algebra (for group theory) and topology.

Physics

Perhaps the subject with the strongest historical ties with mathematics is physics. Certainly some of the great physical theories have been based on novel applications of mathematical theory or the invention of new subjects in the field: Newtonian mechanics and calculus, relativity and Riemannian geometry, quantum theory and functional analysis, etc.

Nearly all mathematics courses offered here at UW Madison will have some applications to physics. The following is a collection of courses which would support general interest in physics.

Biological Sciences

Applications of mathematics to biology has undergone a recent boom. Historically, the biologist was perhaps most interested in applications of calculus, but now nearly any modern area of mathematical research has an application to some biological field[11]. The following lists some possibilities.

Bio-Informatics

Bioinformatics is the application of computational methods to understand biological information. Of course the most interesting items of biological information is genetic and genomic information. Considering that the human genome has over three billion basepairs [12], it's no wonder that many mathematicians find compelling problems in the area to devote their time.

Students with strong mathematical backgrounds who are interested in bioinformatics can find careers as a part of research teams in public and private laboratories across the world [13]. Moreover, many universities have established interdisciplinary graduate programs promoting this intersection of mathematics, biology, and computer science [14].

Students interested in bioinformatics should have a strong background in computational mathematics and probability. Students should also have a strong programming background.

Complete this major with a few additional courses if you are interested in medical school [15].

Bio-Statistics

Biostatistics is the application of mathematical statistical methods to areas of biology. Historically, one could consider the field to have been founded by Gregor Mendel himself. He used basic principles of statistics and probability to offer a theory for which genetic traits would arise from cross hybridization of plants and animals. His work was forgotten for nearly fifty years before it was rediscovered and become an integral part of modern genetic theory.

Beyond applications to genetics, applications of biostatistics range from public health policy to evaluating laboratory experimental results to tracking population dynamics in the field. Currently, health organizations consider there to be a shortage of trained biostatisticians[16]. Students interested in this area should find excellent job prospects.

Students interested in biostatistics should have strong backgrounds in probability, statistics, and computational methods.

Stat 333 has as a prerequisite some experience with statistical software. This can be achieved by also registering for Stat 327. Stat 327 is a single credit course which does not count for the mathematics major.

Ecology, Forestry, Wildlife Ecology

Applications of advanced mathematics to ecology has resulted in science's improved ability to track wild animal populations, predict the spread of diseases, model the impact of humans on native wildlife, control invasive species, and more. Modeling in this area is mathematically interesting due to the variety of scales and the inherent difficulty of doing science outside of a laboratory! As such the methods of deterministic and stochastic models are particularly useful.

Genetics

Applications of mathematics in genetics appear on a wide range of scales: chemical processes, cellular processes, organism breeding, and speciation. For applications of mathematics in genetics on the scale of chemical processes you might want to examine the suggested packages for bioinformatics or structural biology. If instead you are interested in the larger scale of organisms you might consider the package in biostatistics or the one below:

Structural Biology

Structural biologists are primarily interested in the large molecules which are involved in cellular processes: the fundamental chemical building blocks of life. The field lies on the intersection of biology, physics, chemistry, and mathematics and so structural biology is an exciting area of interdisciplinary research.

In general, the mathematics involved in structural biology is focused on computational methods, probability, and statistics. Note that we offer a specialized course in Mathematics Methods in Structural Biology - Math 606.

Systems Biology

Systems biology is the computational and mathematical modeling of biological systems at any scale. The classical example of this may be the predator-prey model of differential equations which describe the relative population dynamics of two species. Other systems examples include disease transmission, chemical pathways, cellular processes, and more.

In general, the mathematics involved in systems biology is focused on computational methods, dynamical systems, differential equations, the mathematics of networks, control theory, and others. Note that we offer a specialized course in Mathematical Methods in Systems Biology - Math 609.

Engineering

Engineering is the application of science and mathematics to the invention, improvement, and maintenance of anything and everything. As with many of the sciences, engineers and mathematicians have a symbiotic relationship: Engineers use mathematics to make new things; the new things exhibit novel properties that are mathematically interesting.

In general all of mathematics can be applied to some field of engineering. However the programs offered below are not substitutes for engineering degrees. That is, student who are interested in an engineering career upon completion of their undergraduate degree should probably enroll in one of the engineering programs offered by the College of Engineering. Similarly, students who are primarily interested in mathematics might instead choose an option I major and concentrate their upper level coursework in applied mathematics. Students who are truly interested in both areas should consider the degree program in Applied Mathematics, Engineering, and Physics.

So who do the programs below serve? They serve engineering students who wish to take a second major in mathematics. In general such students are excellent candidates for graduate study in engineering.

Chemical Engineering

The following program details an option 2 package for students in the College of Engineering program in Chemical Engineering who are interested in pursuing a second major in mathematics.

Civil Engineering

The following program details an option 2 package for students in the College of Engineering program in Civil and Environmental Engineering who are interested in pursuing a second major in mathematics.

Math 531 is advanced probability and may be taken only after Math 421 or Math 521.

Electrical and Computer Engineering

The following program details an option 2 package for students in the College of Engineering program in Computer and Electrical Engineering who are interested in pursuing a second major in mathematics.

Engineering Mechanics and Astronautics

The following program details an option 2 package for students in the College of Engineering program in Engineering Mechanics and Astronautics who are interested in pursuing a second major in mathematics.

Computer Science

Computer science as an independent discipline is rather young: The first computer science degree program offered in the United States was formed in 1962 (at Purdue University). Despite its youth, one could argue that no single academic discipline has had more of an effect on human society since the scientific revolution.

Since computer science is foremost concerned with the theory of computation, its link with mathematics is robust. Historical examples include Alan Turing, A mathematician and WWII cryptoanalyst who's theory of the Universal Turing Machine forms the central framework of modern computation; and John Von Neumann, A mathematician who's name is ascribed to the architecture still used for nearly all computers today.[20] There are broad overlaps in reasearch in the two fields. For example, one of the most famous unsolved problems in mathematics, the P vs NP problem, is also considered an open problem in the theory of computation.

Since computer science is a full field enveloping philosophy, mathematics, and engineering there are many possible areas of interest which a student of mathematics and computer science might focus on. Below are several examples.

Computational Methods

Computational methods are the algorithms a computer follows in order to perform a specific task. Of interest besides the algorithms is methods for evaluating their quality and efficiency. Since computational mathematics is on the interface between pure and applied methods students who concentrate in this area can find many exciting research opportunities available at the undergraduate level.

The mathematical coursework focuses on combinatorics, analysis, and numerical methods.

Theoretical Computer Science

If you are interested in a more theoretical bend to your studies, follow the program above but with the following changes:

Include both CS 520 and CS 577 into your core applied courses.

Replace the two computational methods courses with Math 567 and Math 571.

Cryptography

Due to the widespread use of computer storage, platforms, and devices; security is now of singular interest. Students with expertise in the mathematics associated with cryptography can find interesting opportunities after graduation in public and private security sectors.

The mathematics associated to secure messaging and cryptography is typically centered on combinatorics and number theory.

Secondary Education

The so called STEM fields continue to be a major area of interest and investment for education policy makers. In particular secondary education instructors with strong mathematics backgrounds are in demand across the nation in public, private, and charter school environments.

The following program was designed for a math major who is interested in becoming an educator at the secondary level. Note that successful completion of the coursework outlined below would make a strong candidate for graduate work in mathematics and education at the masters level. Our own School of Education offers a Masters Degree in Secondary Mathematics which concludes with state certification.

Note that a major requires at least two courses at the 500 level. Therefore you should consider the suggestions below carefully.

Courses in computer programming, statistics, physics, economics, and finance can broaden your content areas and qualify you for more subjects.

Statistics

Statistics is the study of the collection, measuring, and evaluation of data. Recent advances in our ability to collect and parse large amounts of data has made the field more exciting then ever before. Positions in data analysis are becoming common outside of laboratory environments: marketing, education, health, sports, infrastructure, politics, etc.

Statistics has a strong relationship with mathematics. The areas of mathematics of particular interest are linear algebra, probability, and analysis.